Express this quotient in scientific notation: ${\frac{5.320\times 10^{-2}} {7.0\times 10^{-4}}}$
Solution: Start by collecting like terms together. $= {\frac{5.320} {7.0}} \times{\frac{10^{-2}} {10^{-4}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.76 \times 10^{-2\,-\,-4}$ $= 0.76 \times 10^{2}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.76$ is the same as $7.60 \div 10$ , or $7.60 \times 10^{-1}$ $ = {7.60 \times 10^{-1}} \times 10^{2} $ $= 7.60\times 10^{1}$